Vorträge in der Woche 24.11.2025 bis 30.11.2025

Dienstag, 25.11.2025: Schottky and quasi-Fuchsian groups, Hitchin representations and higher Teichmüller theory

Daniel Funck

Mittwoch, 26.11.2025: The 1-fold tropical Abel-Prym map

Giusi Capobianco (Roma Tor Vergata)

The algebraic Abel-Prym map relates the geometry of a double cover of algebraic curves with their corresponding Prym varieties. Birkenhake and Lange proved that the map has degree 2 if and only if the source curve is hyperelliptic. In the talk I will present joint work with Yoav Len, in which we investigate the 1-fold Abel-Prym map in the tropical setting and prove similar results. I will show that the tropical Abel-Prym map is a harmonic morphism of degree 2 if and only if the source graph is hyperelliptic. Furthermore, I will prove that the Jacobian of the image of this map is isomorphic, as pptav, to the Prym variety of the cover and relate this result to the tropical bigonal construction.

Donnerstag, 27.11.2025: On the Perturbation of Photon Surfaces

Simone Coli (Universität Tübingen)

It is well known that many static, spherically symmetric space-times admit a photon sphere, with the Schwarzschild solution serving as the canonical example. The notion of a photon sphere can be generalized to that of a photon surface, in the sense of Claudel–Virbhadra–Ellis. The uniqueness of static space-times containing an equipotential photon surface has been rigorously established, in both vacuum and electro-vacuum cases, in works by C. Cederbaum and G. Galloway and by C. Cederbaum, S. Jahns, and O. Vicanek Martinez. Furthermore, the uniqueness of space-times containing a photon sphere has been studied under non-spherical perturbations of the Schwarzschild metric, under the assumption of a constant lapse function and allowing for simultaneous deformations of the spatial geometry and of the photon sphere’s location, in work by H. Yoshino. Building upon these results, we investigate the stability and deformation of photon surfaces when the lapse function is no longer assumed to be constant, and we study the behaviour of photon surfaces in the Schwarzschild space-time under small non-spherical perturbations of the full static data.